Diagonalization and representation results for nonpositive sesquilinear form measures
Functional Analysis
2015-05-13 v1
Abstract
We study decompositions of operator measures and more general sesquilinear form measures into linear combinations of positive parts, and their diagonal vector expansions. The underlying philosophy is to represent as a trace class valued measure of bounded variation on a new Hilbert space related to . The choice of the auxiliary Hilbert space fixes a unique decomposition with certain properties, but this choice itself is not canonical. We present relations to Naimark type dilations and direct integrals.
Keywords
Cite
@article{arxiv.0706.2121,
title = {Diagonalization and representation results for nonpositive sesquilinear form measures},
author = {Tuomas Hytonen and Juha-Pekka Pellonpaa and Kari Ylinen},
journal= {arXiv preprint arXiv:0706.2121},
year = {2015}
}
Comments
J. Math. Anal. Appl., in press